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The members of the algebra may be decomposed by grade (as in the formalism of differential forms) and the (geometric) product of a vector with a k-vector decomposes into a (k − 1)-vector and a (k + 1)-vector. The (k − 1)-vector component can be identified with the inner product and the (k + 1)-vector component with the outer product. It is ...
The density of the linear momentum of the electromagnetic field is S/c 2 where S is the magnitude of the Poynting vector and c is the speed of light in free space. The radiation pressure exerted by an electromagnetic wave on the surface of a target is given by P r a d = S c . {\displaystyle P_{\mathrm {rad} }={\frac {\langle S\rangle }{\mathrm ...
where: is the rate of change of the energy density in the volume. ∇•S is the energy flow out of the volume, given by the divergence of the Poynting vector S. J•E is the rate at which the fields do work on charges in the volume (J is the current density corresponding to the motion of charge, E is the electric field, and • is the dot product).
So, dimensionally, the Poynting vector is S = power / area = rate of doing work / area = ΔF / Δt Δx / area , which is the speed of light, c = Δx / Δt, times pressure, ΔF / area.
The Poynting vector for a wave is a vector whose component in any direction is the irradiance (power per unit area) of that wave on a surface perpendicular to that direction. For a plane sinusoidal wave the Poynting vector is 1 / 2 Re{ E × H ∗ } , where E and H are due only to the wave in question, and the asterisk denotes ...
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum.It is a three-dimensional form of the wave equation.
The electromagnetic tensor, conventionally labelled F, is defined as the exterior derivative of the electromagnetic four-potential, A, a differential 1-form: [1] [2] = . Therefore, F is a differential 2-form— an antisymmetric rank-2 tensor field—on Minkowski space. In component form,